The joint creeping motion of three viscid liquids in a plane layer: A priori estimates and convergence to steady flow
- Authors: Andreev V.K.1,2, Cheremnykh N.1,2
-
Affiliations:
- Institute of Computational Modelling
- Siberian Federal University
- Issue: Vol 10, No 1 (2016)
- Pages: 7-20
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212218
- DOI: https://doi.org/10.1134/S1990478916010026
- ID: 212218
Cite item
Abstract
We study a partially invariant solution of rank 2 and defect 3 of the equations of a viscid heat-conducting liquid. It is interpreted as a two-dimensional motion of three immiscible liquids in a flat channel bounded by fixed solid walls, the temperature distribution on which is known. From a mathematical point of view, the resulting initial-boundary value problem is a nonlinear inverse problem. Under some assumptions (often valid in practical applications), the problem can be replaced by a linear problem. For the latter we obtain some a priori estimates, find an exact steady solution, and prove that the solution approaches the steady regime as time increases, provided that the temperature on the walls stabilizes.
About the authors
V. K. Andreev
Institute of Computational Modelling; Siberian Federal University
Author for correspondence.
Email: andr@icm.krasn.ru
Russian Federation, Akademgorodok 50, bld. 44, Krasnoyarsk, 660036; pr. Svobodnyi 79, Krasnoyarsk, 660041
N. Cheremnykh
Institute of Computational Modelling; Siberian Federal University
Email: andr@icm.krasn.ru
Russian Federation, Akademgorodok 50, bld. 44, Krasnoyarsk, 660036; pr. Svobodnyi 79, Krasnoyarsk, 660041